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Finite p-groups with normal normalisers

Published online by Cambridge University Press:  17 April 2009

Elizabeth A. Ormerod  and
Gemma Parmeggiani
Elizabeth A. Ormerod
Affiliation:
Department of Mathematics, Mathematical Sciences Institute, The Australian National University, Canberra ACT 0200, Australia
Gemma Parmeggiani
Affiliation:
Dip. di Matematica Pura ed Appl., via Belzoni 7, Università degli Studi di Padova, 35131 Padova, Italy
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We consider the class N of groups in which the normaliser of every subgroup is normal, and the class C of groups in which the commutator subgroup normalises every subgroup. It is clear that C ⊆ N, and it is known that groups in the class N are nilpotent of class at most 3. We show that every finite p-group in N is also in C, provided that p ≥ 5, and we give an example showing that this is not true for p = 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 141 - 150
Copyright
Copyright © Australian Mathematical Society 2004

References

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